Read e-book online 30 Days to Market Mastery PDF

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If the effect of increasing expected growth rates on stocks when the interest rate is higher was taken into account, the option price would have been even less. This shows that option prices differ as the interest rate differs. The price of a put option is less if the interest rate is higher, and for a call option the reverse holds. 2, this effect will be discussed in more detail. 1 shows in which way the prices of an at-the-money call and put option vary with interest rate. Note that if the interest rate is 0 the prices of an at-the-money call and put option are the same, which is perfectly in compliance with the put–call parity.

The Black–Scholes formula uses the following notation: ct ¼ Price of a European call option at time t; pt ¼ Price of a European put option at time t; St ¼ Price of the underlying stock at time t; T À t ¼ Time to maturity; K ¼ Strike price of the option; ¼ Volatility of the underlying stock; r ¼ Interest rate: The prices, at time t, of a European call option ct and a European put option pt are given by: ct ¼ St Nðd1 Þ À K eÀrðTÀtÞ Nðd2 Þ; ð2:1Þ pt ¼ K eÀrðTÀtÞ NðÀd2 Þ À St NðÀd1 Þ ð2:2Þ In these formulae, NðxÞ is the standard Normal distribution, and d1 , d2 are defined as: À Á St ln þ r þ 12 2 ðT À tÞ K pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ d1 ¼ ð2:3Þ TÀt pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð2:4Þ d2 ¼ d1 À T À t Of course, the above formulae reflect the fact that the price of an option on a non-dividend paying stock depends on the strike price, price of the underlying stock, time to maturity, volatility of the underlying stock and the 28 AN INTRODUCTION TO OPTIONS TRADING interest rate.

It follows that in this case the American put option should be exercised immediately. 2 3 Argument on p. 158 of Hull (1993). The following argument is based on pp. 160=161 of Hull (1993). 5 15 PAYOFFS The examples show that the payoff of an option can never be negative, since the holder can decide not to exercise his option right. This does not mean that the profit of the owner of an option cannot be negative. This is of course because an initial price has been paid for the option. So, a distinction has to be made between the profit of an option and the payoff.